LCM of 7 and 28 is 72. The smallest number among all common multiples of 7 and 28 is the LCM of 7 and 28. (7, 14, 21, 28, 35, 42, etc.) and (28, 56, 84, 112, 140, 168, etc.) are the first few multiples of 7 and 28. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 7 and 28?
The answer to this question is 28. The LCM of 7 and 28 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 7 and 28, is the smallest positive integer 28 which is divisible by both 7 and 28 with no remainder.
How to Find LCM of 7 and 28?
LCM of 7 and 28 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7 and 28 Using Prime Factorisation Method
The prime factorisation of 7 and 28, respectively, is given by:
(7) = 71 and (2 × 2 × 7) = 22 × 71
LCM (7, 28) = 28
LCM of 7 and 28 Using Division Method
We’ll divide the numbers (7, 28) by their prime factors to get the LCM of 7 and 28 using the division method (preferably common). The LCM of 7 and 28 is calculated by multiplying these divisors.
| 2 | 7 | 28 |
| 2 | 7 | 14 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (7, 28) = 28
LCM of 7 and 28 Using Listing the Multiples
To calculate the LCM of 7 and 28 by listing out the common multiples, list the multiples as shown below
| Multiples of 7 | Multiples of 28 |
| 7 | 28 |
| 14 | 56 |
| 21 | 84 |
| 28 | 112 |
| 35 | 140 |
The smallest common multiple of 7 and 28 is 28.
Therefore LCM (7, 28) = 28
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LCM of 7 and 28 Solved Example
Question: The product of two numbers is 196. If their GCD is 7, what is their LCM?
Solution:
Given: GCD = 7
product of numbers = 196
LCM × GCD = product of numbers
LCM = Product/GCD = 196/7
Therefore, the LCM is 28.
The probable combination for the given case is LCM(7, 28) = 28.
Frequently Asked Questions on LCM of 7 and 28
What is the LCM of 7 and 28?
List the methods used to find the LCM of 7 and 28.
If the LCM of 28 and 7 is 28, Find its GCF.
Since the LCM of 28 and 7 = 28
⇒ 28 × GCF(28, 7) = 196
Therefore, the greatest common factor (GCF) = 196/28 = 7.
How to Find the LCM of 7 and 28 by Prime Factorization?
⇒ LCM of 7, 28 = 2 × 2 × 71 = 28.
What is the Least Perfect Square Divisible by 7 and 28?
LCM of 7 and 28 = 2 × 2 × 7 [Incomplete pair(s): 7] ⇒ Least perfect square divisible by each 7 and 28 = LCM(7, 28) × 7 = 196 [Square root of 196 = √196 = ±14] Therefore, 196 is the required number.
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